Curvature continuous corner cutting
- Hormann , Kai ORCID Facoltà di scienze informatiche, Università della Svizzera italiana, Svizzera
- Mancinelli, Claudio ORCID DIBRIS, Università degli Studi di Genova, Italy
- 2024
Published in:
- Computer aided geometric design. - 2024, vol. 114, no. 102392
English
Subdivision schemes are used to generate smooth curves by iteratively refining an initial control polygon. The simplest such schemes are corner cutting schemes, which specify two distinct points on each edge of the current polygon and connect them to get the refined polygon, thus cutting off the corners of the current polygon. While de Boor (1987) shows that this process always converges to a Lipschitz continuous limit curve, no matter how the points on each edge are chosen, Gregory and Qu (1996) discover that the limit curve is continuously differentiable under certain constraints. We extend these results and show that the limit curve can even be curvature continuous for specific sequences of cut ratios.
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- English
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- Mathematics
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- CC BY
- Open access status
- hybrid
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- DOI 10.1016/j.cagd.2024.102392
- ARK ark:/12658/srd1331165
- Persistent URL
- https://n2t.net/ark:/12658/srd1331165
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